The vendor did get the hint, and the second iteration of the device did slowly warm up the pumps so this process would no longer be required.
https://onccy.com/how-to-choose-between-type-a-b-c-and-d-min...
Notoriously a crescent wrench makes an excellent 1000A slow blow fuse
You can observe this with a speed control knob/ESP32 where a running fan will happily run forever with the knob turned down to e.g. a 30% duty cycle. But after turning to 0% and waiting for the blades to fully stop, if set back to the same 30% they won't move at all or you'll maybe hear a sketchy clicking/whine sound with the blades intermittently twitching.
It's sort of a solved problem - the ones I'm aware of are things like LynTec sequenced panels built exactly for this, and Siemens' SENTRON semiconductor CBs where you can control then curve to your spec.
Convincing stakeholders though, is almost a job of its own.